The lateral area of a frustum of a regular triangular pyramid is 1,081cm^2, and the altitude and lateral edges are 24cm and 26cm, respectively. Find the lengths of the sides of the bases.

Question

Mathematics

Sterling Wang

21 May, 21:46

The lateral area of a frustum of a regular triangular pyramid is 1,081cm^2, and the altitude and lateral edges are 24cm and 26cm, respectively. Find the lengths of the sides of the bases.

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Answers (2)

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Tommy Lowe · Answer 1

Lateral Area = 3 * (a + b) / 2 * 24

1,081 = 36 * (a + b) / : 36

a + b ≈ 30

((a - b) / 2) ² = 26 ² - 24² = 676 - 576 = 100

(a - b) / 2 = 10

a - b = 20

a = b + 20

a + b = 30

2 b + 20 = 30

2 b = 10

b = 10 : 2

b = 5 cm

a = 5 + 20

a = 25 cm

Landin Jarvis · Answer 2

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